If you are single (i.e. unmarried, widowed or divorced) with no children or grandchildren your property goes:
To your parents or whichever one is living: if both your parents are dead, to your brothers and sisters, and if any of your brothers or sisters are dead, the share of that brother or sister goes to any of their children who survive you: if both of your parents are dead and you have no surviving brothers, sisters, nieces or nephews, then to any half brothers or sisters (and if any of them are dead, their share goes to any of their children who survive you): if none of the above survive you, then your grandparents and then to any aunts or uncles and after that to various more distant relatives: if you have no relatives, or only very distant ones, your property then goes to the crown (i.e. the government).
If you are single with children or grandchildren your property goes:
To your children in equal shares: but if any of them have died their share will be divided between any of their children.
If you are married with no children or grandchildren:
The first £450,000 of your property goes to your husband or wife plus one half of the remainder: the other half goes to your parents or whichever one is living: if both parents are dead, the other half will go to your brothers or sisters or, as above, to the children of any who have died before you: if none of the above survives you, then your husband or wife gets everything.
If you are married with children or grandchildren:
The first £250,000 of your property goes to your husband or wife plus a life interest in one half of the remainder (this will eventually pass to your children or grandchildren on his or her death): the other half goes directly to your children or, as above, to the children of any who have died before you.
When these rules are applied it usually does not matter whether a person is legitimate, illegitimate or adopted. Thus, for example, your adopted children have the same rights as your natural children, and the same is true for any of your children whose mother is not your wife or whose father is not your husband.